Correction to Faulty Traditional Unintentionally Bayesian Formula for Device Reliability Estimation

This paper presents a fundamental correction to a decades-long standing traditional formula for computing confidence bounds on failure rates estimated from reliability life test evaluations. The chi-squared based formula with degrees of freedom set to twice the number of observed failures plus two imprecisely overestimates the failure rate confidence bound by failing to place the observed maximum likelihood estimate hazard function value at the median of the posterior distribution. Correcting this formula involves shifting from Bayes-Laplace prior with unity adder to the neutral Kerman prior with adder one-third. The repaired formula requires expression in native Gamma distribution form since the erstwhile equivalent degrees of freedom for chi-squared representation is disallowed as it is non-integer. Improvements in the accuracy of the confidence bound are more marked for lower numbers of life test evaluation failures.